Quasi-steady criteria

The short-time criterion is the more stringent except when H 1 and p/ 1. External resistance controls and the concentration within the particle is uniform when the inequalities in Eqs. (3-74) and (3-75) are reversed. Even if the external resistance is not negligible relative to the internal resistance, it may be possible to assume constant external resistance, i.e., quasi-steady behavior. Comparison... 

This ratio provides the criterion for the applicability of the quasi-steady-state approximation for the concentration as shown in Table V. 

By splitting the quasi-steady-state assumption of diffusion of particles under the action of the interaction force field into two parts, kinetic equations which account for accumulation at both the primary and secondary minimum are formulated. Conditions are established under which, after a short transient, reversible adsorption or coagulation can be treated by neglecting accumulation at the secondary minimum. The effect of tangential velocity of particles on the rate of reversible adsorption is analyzed and a criterion established when the effect... 

The ILDM technique proposed by Maas and Pope overcomes this problem by describing geometrically the optimum slow manifold of a system. The criterion for reduction is based on the time-scales of linear combinations of variables and not on species themselves. The main advantage of the technique is that it requires no information concerning which reactions are to be assumed in equilibrium or which species in quasi-steady-state. The only inputs to the system are the detailed chemical mechanism and the number of degrees of freedom required for the simplified scheme. The ILDM method then tabulates quantities such as rates of production on the lower-dimensional manifold. For this reason, it is necessarily better suited to numerical problems since it does not result in sets of rate... 

A number of techniques was developed to solve the optimization problem. Some deal with two limiting cases of periodic operation relaxed steady states obtained at high fi-equency of the forcing function and quasi-steady states with forcing period much longer than the system response time [18]. For the intermediate range of frequencies and low amplitudes, the most widely used method is the IT-criterion developed by Guardabassi et. al., [19]. This method have been used in Refs. 20-22 for analysis of chemical reaction systems. 

It is to be noted that the criterion for ill-posedness is affected only by the terms which are proportional to the gradients of h, u, u (derivatives with respect to time and space) and, therefore, apparently unaffected by the quasi-steady modelling of the shear stresses. However, the test for well-posedness is carried out on a stratified wavy configuration, which is represented by the averaged values of H, U, (obtained from the solution of AF = 0, Equation 11). Obviously, their values depend on the models used for the wall and interfacial shear stresses. In particular, the modelling of x. deserves a special attention since in the wavy regime the augmentation of the interfacial friction factor, due to the interfacial waviness is to be considered. 

Lu, T., Law, C.K. A criterion based on computational singular perturbation for the identification of quasi steady state species a reduced mechanism for methane oxidation with NO chemistry. Combust. Flame 154, 761-774 (2008a)... 

We summarize our findings. It is suggested the criterion of critical condition, that is, the extremal behavior of the reaction species concentration, may be applied to reveal the critical conditions of nonlinear chemical dynamic systems. This is with the changeover of different dynamic modes of the reactions, such as the quasi-periodic and chaotic oscillations of the intermediate concentrations, as well as the steady-state mode. At the same time the Hamiltonian formalism makes it possible not only to have a successful numerical identification of the critical reaction conditions, but also to specify the role of individual steps of the reaction mechanism under different conditions. 

The squeeze nuabec can be considered as a quantiliquation of Gu s (42) criterion. The reference fila thickness h is the steady state fila thickness under reference speed and reference load conditions. Figs. 10 a and 11a show the quasi-stationary film thickness h t > Fi-9S. 10 b and 11 b present the dynamic behaviour of the minimum film thickness h. / h, and Figs. 10 c and 11 c the... 

When the unsteady-state equations are being integrated forward in time either towards the Eulerian steady state or towards the Lagrangian steady propagation rate, a criterion is required for deciding when the steady situation is achieved. In both cases this is provided by the space integral reaction rates qiA dy, which for sufficiently small finite difference intervals may be replaced by the summations x y)n or an equivalent quantity, where A dy) is the volume of the nth element and A a weighted mean area within the element. For the quasi-one-dimensional steady-state flame we have from Eq. (2.12)... 

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